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Flow Shop with Job–Dependent Buffer Requirements—a Polynomial–Time Algorithm and Efficient Heuristics

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11548))

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Abstract

The paper is concerned with the two-machine flow shop, where each job needs storage space (a buffer requirement) during the entire time of its processing. The buffer requirement is determined by the duration of job’s first operation. The goal is to minimise the time needed for the completion of all jobs. This scheduling problem is NP-hard in the strong sense even for very restricted cases such as the case with a given order of jobs processing on one of the machines. The paper contributes to the efforts of establishing the borderline between the NP-hard and polynomial-time solvable cases by proving that there exists a polynomial-time algorithm which constructs an optimal schedule if the duration of each operation does not exceed one-fifth of the buffer capacity. The presented polynomial-time algorithm is used as a basis for a heuristic for the general case. This heuristic is complemented by a Lagrangian relaxation based heuristic and a bin-packing based constructive heuristic. The heuristics are tested by computational experiments.

A. Kononov—Research of the first author is partially supported by RFBR grant 17-07-00513.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    Alexander Kononov

  2. University of Technology Sydney, PO Box 123, Broadway, NSW, 2007, Australia

    Julia Memar & Yakov Zinder

Authors
  1. Alexander Kononov
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  2. Julia Memar
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  3. Yakov Zinder
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Corresponding author

Correspondence to Julia Memar .

Editor information

Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Kononov, A., Memar, J., Zinder, Y. (2019). Flow Shop with Job–Dependent Buffer Requirements—a Polynomial–Time Algorithm and Efficient Heuristics. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_24

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  • DOI: https://doi.org/10.1007/978-3-030-22629-9_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22628-2

  • Online ISBN: 978-3-030-22629-9

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